Stratified economic optimization prediction control method for rectifying tower

Abstract

The invention discloses a rectifying tower layering economic optimization prediction control method. A double-layer structure prediction control strategy of the rectifying tower comprises an economic self-optimization steady-state optimization layer and a set value tracking dynamic control layer, and aims to meet the economical efficiency and control performance targets at the same time; the steady-state optimization layer solves the optimal objective function of the steady-state model of the rectifying tower under the constraint of output and input values such as the outlet concentration and the reflux quantity of the rectifying tower, and the optimal steady-state input and output with the maximum economic benefits are determined; the dynamic control layer adopts an improved dynamic matrix control algorithm to output the optimal operation variable to the opening degree of a valve or a set value of a traditional PID controller, dynamic tracking control of an optimal set point is achieved, and finally control over multi-target hierarchical prediction of the rectifying tower is completed.

Description

Technical Field

[0001] The present invention belongs to the field of process industry optimization control, and in particular relates to a double-layer predictive control method based on nonlinear model discretization. Background Art

[0002] The distillation tower is a chemical production device with strong nonlinearity and is the core equipment in the chemical production process. The control performance directly affects the production efficiency and product quality. Therefore, many scholars are committed to the study of the control method of the distillation tower. However, the model has complex nonlinearity and there is still no consistent control method for it.

[0003] Although the control method that only considers the control target guarantees product quality, it ignores economic benefits, which is not good for factory production in the long run. The two-level hierarchical control method that uses a steady-state objective function to weight each optimization objective function takes into account the control target and economic benefits, but the priority of each optimization objective function is difficult to guarantee, and there is no certain criterion for the selection of weights. The two-level hierarchical control method that uses model linearization has linearization errors. For a strongly nonlinear, real-time control system such as a distillation tower, the impact of the error cannot be ignored. Therefore, based on the characteristics of the distillation tower model and in view of the shortcomings of the existing distillation tower control method, the present invention proposes a distillation tower hierarchical economic optimization prediction control method. Summary of the invention

[0004] The purpose of the present invention is to propose a stratified economic optimization predictive control method for a distillation tower in view of the strong nonlinearity of the distillation tower and the need to take both control performance and economic indicators into consideration during the production process. The method can handle the impact of disturbances on the control algorithm, avoid linearization of the model, and at the same time ensure control optimization objectives according to priority.

[0005] The object of the present invention is achieved through the following technical scheme: a distillation tower layered economic optimization prediction control method, the method comprising the following steps:

[0006] (1) Establish a steady-state mathematical model of the controlled system of the distillation tower: collect the initial values ​​of the outlet concentration, sensitive plate temperature, reflux flow, and reboiler heating of the distillation tower to construct a steady-state mathematical model of the distillation tower; (2) Under the constraints of the output and input values ​​such as the outlet concentration and reflux flow of the distillation tower, solve the optimal objective function of the steady-state model of the distillation tower to determine the predicted values ​​of the optimal values ​​of the outlet concentration, sensitive plate temperature, reflux flow, and reboiler heating that maximize the economic benefits; (3) Dynamic predictive control of the distillation tower: Finally, according to the control objectives provided by the steady-state optimization layer of the distillation tower, determine the dynamic optimization proposition, and use the improved dynamic matrix control algorithm to output the optimal operating variables to the valve opening or the set value of the traditional PID controller, so as to achieve dynamic tracking control of the optimal set point, and finally complete the multi-objective hierarchical predictive control of the distillation tower.

[0007] Preferably, in step 1, a steady-state mathematical model of the distillation tower is constructed, specifically:

[0008] Collect the initial values ​​of the state variables of the distillation tower: the outlet concentration of the distillation tower and the temperature of the sensitive plate, and input the initial values ​​of the variables: the reflux flow rate and the reboiler heating amount and substitute them into the dynamic model of the distillation tower.

[0009]

[0010] The above system satisfies the following constraints at any sampling time:

[0011]

[0012] Where P is the prediction time domain, is the state vector of the system, is the input vector of the distillation column system, is the output vector of the distillation tower system, e(k) is the error between the measured value y(k) and the predicted value y(k|k-1), y min ≤y max ,u min ≤u max are n-dimensional and m-dimensional vectors respectively.

[0013] The obtained dynamic model is then converted into a steady-state mathematical model of the distillation tower

[0014]

[0015] Among them, ss represents steady state, y ss ,u ss denote the steady-state output and input of the distillation tower system, Δy ss (k+1)=y ss (k+1)-y ss (k) is the steady-state output increment of the system, Δu ss (k) = u ss (k)-u ss (k-1) is the steady-state input increment of the system. Since the increment of the disturbance cannot be measured, Δe is used. ss (k) = e ss (k)-e ss (k-1) to estimate the steady-state error correction Δe ss (k). is the steady-state gain matrix.

[0016] Preferably, the distillation tower steady-state target calculation in step 2 is specifically as follows:

[0017] (2.1) Perform real-time optimization on the global object nonlinear model of the distillation tower to find the optimal solution y * ,u *

[0018]

[0019] (2.2) Use quadratic programming to achieve target tracking of the distillation tower and solve y ss (k+1) and u ss (k)

[0020]

[0021] y * ,u * are the optimal output and input operation targets calculated from the real-time optimization layer, Q and V are positive definite penalty matrices, and u min is the lower limit of the input variable, u max is the upper limit of the input variable, y min is the lower limit of the output variable, y max is the upper limit of the output variable.

[0022] (2.3) Economic optimization, determine the input variable value u of the distillation tower when the economic benefits of the whole plant are maximized ss (k) and the output variable value y ss (k+1).

[0023]

[0024] Among them, J represents the economic optimization goal, c T =[c1,c2,…,c m ] is the standardized parameter of each control variable, and MP is the potential maximum economic benefit value of the system.

[0025] Preferably, the input and output constraints in step 2 are specifically:

[0026] Feasibility analysis and soft constraint adjustment adopt a priority strategy, and the order of relaxing constraints is determined based on a weighted strategy.

[0027]

[0028] Where C is the user-defined relaxation weight coefficient corresponding to the soft constraint with priority 1, I 1 is the corresponding identity matrix. By solving the optimization problem, we can get the relaxation amplitude ε of the constraint with priority 1. 1 , and update b to b update =b+ε 1 .

[0029] Preferably, the dynamic optimization proposition calculation in step 3 is specifically as follows:

[0030]

[0031] Among them, P is the prediction time domain, M is the control time domain, Q, R, S, T are the weight coefficients of the relevant items respectively. ε is the relaxation variable to ensure that there is a feasible solution to the optimization objective function. [u min u max ] is the constraint condition of the input variable, [y min y max ] represents the soft constraint value of the system controlled variable.

[0032] Repeat the above steps continuously to complete the control of multi-objective hierarchical prediction.

[0033] Beneficial effects of the invention: The invention proposes a distillation tower stratified economic optimization predictive control method. Compared with the traditional method, the method is more accurate in processing models, has a better suppression effect on disturbances, and can ensure the optimization target according to priority in steady-state optimization, providing a better method for the control and optimization of distillation towers. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the structure diagram of the advanced control scheme for the dealcoholization tower C1

[0035] Figure 2 Schematic diagram of the two-layer model predictive control algorithm

[0036] Figure 3 Schematic diagram of the double-layer optimized control structure of the dealcoholization tower

[0037] Figure 4 Schematic diagram of the double-layer optimized control structure of the dealcoholization tower ((a) temperature response curve; (b) concentration response curve) DETAILED DESCRIPTION

[0038] There are two controlled variables and two control variables in the process of the dealcoholization tower system. The state space model of the process is:

[0039] δx(k+1)=Aδx(k)+Bδu(k)

[0040] δy(k)=Cδx(k)

[0041] Where δy=[y1y2] T are the sensitive plate temperature of the distillation tower and the concentration of methanol discharged from the bottom of the tower, δu=[u1u2] TThe sampling period is 36s, and the constraints of the system on input and output variables are considered. Dynamic matrix control and double-layer structure predictive control are used to simulate the distillation process of the dealcoholization tower, and the control effects under the two control strategies are compared. The upper and lower limit constraints of the controlled variables are set as follows: the temperature range of the sensitive plate of the dealcoholization tower is 75-80℃, and the soft constraint range is 75.5-79.5℃; the range of the methanol component of the bottom discharge of the dealcoholization tower is 4%-10%, and the soft constraint range is 4.2%-9.5%.

[0042] Therefore, on the basis of the effectiveness of the traditional control loop, an advanced control scheme is designed. The traditional control scheme of the dealcoholization tower C1 is: the upstream material enters the dealcoholization tower C1 through the feed valve, and the condenser pressure is controlled by adjusting the condenser load in the dealcoholization tower C1; the condenser liquid level is controlled by the flow rate of the liquid phase distillate at the top of the tower; the reboiler liquid level is controlled by adjusting the flow rate of the bottom discharge; the sensitive plate (the 19th plate) is controlled by adjusting the heat input to the reboiler; and the advanced control strategy is used to control the key control variables of the system, that is, the methanol concentration of the C1 tower bottom discharge and the temperature of the 19th sensitive plate of the distillation tower are taken as the controlled variables, and the control is carried out by using the reflux flow rate at the top of the tower and the heating amount of the reboiler as the manipulated variables. The advanced control scheme of the dealcoholization tower C1 is shown in the figure below. Figure 1 shown.

[0043] When designing the dynamic matrix control loop of the dealcoholization tower C1 in the ethylene glycol distillation process, the initial setting value of the methanol concentration of the tower C1 outlet is 0.0583, and the initial setting value of the temperature of the nineteenth sensitive plate is 77.65℃.

[0044] After tuning, the main parameters of the dynamic matrix controller are selected as follows: sampling period T is 36s, model truncation length N is 2000, prediction time domain P is 14, control time domain M is 3, error weight matrix Q is 1.5×E, control weight matrix R is E, β=0.6, s=0.57.

[0045] The product quality and process stability can be guaranteed by the multivariable dynamic matrix control method, but in actual production, the energy consumption index of the distillation tower is very strict. In order to reduce energy consumption while ensuring that the distillation tower kettle temperature (the temperature of the 19th sensitive plate) and the concentration of the discharge component in the tower kettle meet the set requirements, the proposed multivariable double-layer structure prediction model predictive control strategy is used to achieve the above requirements. Among them, the distillation tower kettle temperature is an important indicator for checking whether the discharge is qualified. The tower kettle temperature is closely related to the circulating water flow rate and the reboiler heating amount. Under the premise of giving priority to controlling the distillation tower kettle temperature and the discharge component concentration, the controller takes minimizing energy consumption as the second priority control target, and mainly controls the distillation tower kettle temperature and the discharge component concentration. The double-layer structure predictive control strategy includes a steady-state optimization layer of economic self-optimization and a dynamic control layer of set value tracking, aiming to meet both economic and performance control targets.

[0046] In the energy consumption optimization of the distillation process of the dealcoholization tower, the first indicator is to ensure that the temperature of the distillation tower is within the soft constraint range and the methanol component of the top and bottom discharges is within the soft constraint range. Under this premise, the reflux rate and the heating amount of the reboiler are optimized. In order to achieve this goal, a two-layer control strategy can be adopted, in which the upper steady-state optimization layer is used to optimize economic indicators, and the lower control is used to achieve dynamic performance control. In the upper steady-state optimization, the quadratic programming function is used to solve the optimization function of the economic indicators with constraints. By solving the economic optimization problem, the steady-state target of the controlled variable and the steady-state target of the operating variable are obtained as the set value. In the lower control, the dynamic matrix control algorithm is used to achieve dynamic performance control. Figure 2 and Figure 3 They are respectively a schematic diagram of the double-layer model predictive control algorithm and a schematic diagram of the double-layer optimization control structure of the dealcoholization tower. The sensitive plate temperature and reflux flow set value of the real-time optimization layer are updated to the lower-layer dynamic matrix control algorithm to achieve dynamic control of the reflux flow and reboiler heating.

[0047] In summary, the double-layer structure predictive control method of DMC based on LP economic indicators is expressed as follows:

[0048]

[0049] Among them, k is the sampling time of the system, P is the prediction time domain, M is the control time domain, Q, R, S, T, V, W are the weight coefficients of the relevant items respectively. min u max ,[Δu min Δu max ]] is the constraint condition of input variables and their changes, [y min y max ] represents the soft constraint value of the system controlled variable, [y MIN ,y MAx] represents the hard constraint value of the system controlled variable, ε is the soft constraint relaxation variable of the output variable, A ss is the steady-state gain model of the system.

[0050] The double-layer predictive control runs at the same frequency, avoiding the generation of steady-state errors. The double-layer control strategy can take into account both economic and dynamic performance, and optimize the energy consumption of the dealcoholization tower within a safe and stable range. Add random feed disturbances to test the control performance of the system in the face of unknown interference. Figure 4 (a) represents the temperature response curve under random feed disturbance. It can be seen that when the system faces random feed disturbance, the temperature change of the sensitive plate of the dealcoholization tower is small under the two control strategies and is controlled within an acceptable range. Figure 4 (b) shows the control response of the methanol concentration in the dealcoholization tower outlet. It can be seen that under the two control strategies, the change of the methanol concentration in the tower bottom outlet is small and is controlled within a certain range.

Claims

1. A method for predicting and controlling the economic optimization of distillation tower stratification, characterized by comprising the following steps: (1) Establishing the distillation tower steady-state optimization layer: Collecting the initial values ​​of the distillation tower outlet concentration, sensitive plate temperature, reflux flow, and reboiler heating to construct a steady-state mathematical model of the distillation tower; (2) Steady-state target solution: Solve the optimal objective function of the steady-state mathematical model of the distillation tower under the constraints of the output and input values ​​including the outlet concentration and reflux flow of the distillation tower to determine the predicted values ​​of the outlet concentration, sensitive plate temperature, reflux flow, and optimal reboiler heating value that maximize the economic benefits; (3) Dynamic predictive control of the dynamic control layer of the distillation tower: Finally, the dynamic optimization proposition is determined based on the control objectives provided by the steady-state optimization layer of the distillation tower. The control algorithm is used to output the optimal operating variable to the valve opening or the set value of the traditional PID controller, thereby achieving dynamic tracking control of the optimal set point and finally completing the multi-objective hierarchical predictive control of the distillation tower.

2. A distillation tower layered economic optimization prediction control method according to claim 1, characterized in that In step (1), a steady-state mathematical model of the distillation tower is constructed, specifically: (1.1) Collect the initial values ​​of the state variables of the distillation tower: the outlet concentration of the distillation tower and the temperature of the sensitive plate, and input the initial values ​​of the variables: the reflux rate and the reboiler heating amount, and substitute them into the dynamic model of the distillation tower: The above system satisfies the following constraints at any sampling time: Where A represents the state matrix of the distillation tower system, B represents the control matrix of the distillation tower system, C represents the output matrix of the distillation tower system, P is the prediction time domain, is the state vector of the system, is the input vector of the distillation column system, is the output vector of the distillation tower system, They are represented as real vectors of p, m, and n dimensions respectively. y(k|k-1) represents the output prediction value at time K-1 for time K. e(k) is the error between the measured value y(k) and the predicted value y(k|k-1). min ≤y max ,u min ≤u max are n-dimensional and m-dimensional vectors respectively; (1.2) The obtained dynamic model is then transformed into a steady-state mathematical model of the distillation tower: Among them, ss represents steady state, y ss ,u ss denote the steady-state output and input of the distillation tower system, Δy ss (k+1)=y ss (k+1)-y ss (k) is the steady-state output increment of the system, Δu ss (k) = u ss (k)-u ss (k-1) is the steady-state input increment of the system. Since the increment of the disturbance cannot be measured, Δe is used. ss (k) = e ss (k)-e ss (k-1) to estimate the steady-state error correction Δe ss (k); is the steady-state gain matrix.

3. The method according to claim 1, characterized in that The specific process of solving the steady-state target of the distillation tower in step (2) is as follows: (2.1) Perform real-time optimization on the global object nonlinear model of the distillation tower to find the optimal solution y * ,u * MinJ=f(y,u) Solve the above problem to get the optimal solution: y = y * ,u=u * , J is the real-time optimization objective, g1 is the stability constraint, g2 is the feasibility constraint; (2.2) Use quadratic programming to achieve target tracking of the distillation tower and solve y ss (k+1) and u ss (k) Determine the input variable u ss and the output variable y ss The predicted value u at time k for time k+1 ss (k) and y ss (k+1) y * ,u * are the optimal output and input operation targets calculated from the real-time optimization layer, Q and V are positive definite penalty matrices, and u min is the lower limit of the input variable, u max is the upper limit of the input variable, y min is the lower limit of the output variable, y max is the upper limit of the output variable; (2.3) Economic optimization, determine the optimal input variable value u of the distillation tower when the economic benefits of the whole plant are maximized ss (k) and the optimal output variable value y ss (k+1): Among them, J represents the economic optimization goal, c T =[c1,c2,…,c m ] is the standardized parameter of each control variable, and MP is the potential maximum economic benefit value of the system.

4. The method according to claim 1, characterized in that ,The soft constraint strategy in the input and output constraints in step (2) is specifically: A priority strategy is used to determine the order of relaxing constraints based on a weighted strategy: Where C is the user-defined relaxation weight coefficient corresponding to the soft constraint with priority 1, I 1 is the corresponding identity matrix. By solving the optimization problem, we can get the relaxation amplitude ε of the constraint with priority 1. 1 , and update b to b update =b+ε 1 .

5. The method according to claim 1, characterized in that , the dynamic optimization proposition in step (3) is specifically: Among them, Δu M(k) J(k) represents the dynamic optimization proposition, P is the prediction time domain, M is the control time domain, Q, R, S, T are the weight coefficients of the relevant items respectively; ε is the relaxation variable to ensure that the optimization objective function has a feasible solution; [u min u max ] is the constraint condition of the input variable, [y min y max ] represents the soft constraint value of the system controlled variable, w(k) is the set value vector, It is expressed as the predicted value of the output under the control input of M steps in the future P moments. is the initial prediction value vector, A is the step response test coefficient matrix, △u M (k), Δu M (k+i) represents the increment of the input variable at time k and k+i respectively, represents the output variable at time k+j, u set Indicates the set value of the input variable, u M (k) represents the predicted value of the input under the action of the M-step control output.

6. The method according to claim 3, characterized in that ,The dynamic matrix control algorithm adopted in step (3) is specifically: Introducing a function similar to the exponential function into The prediction vector of the feedback correction part shown in the figure; the variables of the new function can change with the sampling frequency and can achieve convergence in a discrete system. The new error correction matrix is ​​expressed as H′=β n H, where n = 0, 1, ..., N; β ∈ (0, 1), and the new prediction vector is expressed as In the formula Based on this, a compensation correction parameter s is introduced to improve the shift matrix S0, then the corrected prediction vector In the shift array In the last row, the elements in the last two columns are non-zero, and the other elements are all zero; in the other rows, only one element is 1, and all the other elements are 0.

7. The method according to claim 6, characterized in that The controller parameter determination principle of the distillation tower in step (3) using the dynamic matrix control algorithm is as follows: a. Determine the cutoff length N and sampling period T of the distillation tower model; b. Determine the control time domain M, the temperature of the sensitive plate, the control time domain of the liquid level is selected as M=4~8, and the control time domain of the flow rate and pressure is selected as M=2~4; c. Preliminary determination of the distillation tower error weight matrix Q, control weight matrix R, and feedback correction coefficient H; d. Preliminary determination of the distillation tower prediction time domain P; e. Is the performance of the closed-loop system of the distillation tower satisfactory at this time? f. If you are not satisfied, return to step c and redefine the distillation tower controller parameters until you are satisfied.

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